# connected.lpp: Connected Components of a Point Pattern on a Linear Network In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

## Description

Finds the topologically-connected components of a point pattern on a linear network, when all pairs of points closer than a threshold distance are joined.

## Usage

 ```1 2``` ```## S3 method for class 'lpp' connected(X, R=Inf, ..., dismantle=TRUE) ```

## Arguments

 `X` A linear network (object of class `"lpp"`). `R` Threshold distance. Pairs of points will be joined together if they are closer than `R` units apart, measured by the shortest path in the network. The default `R=Inf` implies that points will be joined together if they are mutually connected by any path in the network. `dismantle` Logical. If `TRUE` (the default), the network itself will be divided into its path-connected components using `connected.linnet`. `...` Ignored.

## Details

The function `connected` is generic. This is the method for point patterns on a linear network (objects of class `"lpp"`). It divides the point pattern `X` into one or more groups of points.

If `R=Inf` (the default), then `X` is divided into groups such that any pair of points in the same group can be joined by a path in the network.

If `R` is a finite number, then two points of `X` are declared to be R-close if they lie closer than `R` units apart, measured by the length of the shortest path in the network. Two points are R-connected if they can be reached by a series of steps between R-close pairs of points of `X`. Then `X` is divided into groups such that any pair of points in the same group is R-connected.

If `dismantle=TRUE` (the default) the algorithm first checks whether the network is connected (i.e. whether any pair of vertices can be joined by a path in the network), and if not, the network is decomposed into its connected components.

## Value

A point pattern (of class `"lpp"`) with marks indicating the grouping, or a list of such point patterns.

## Author(s)

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`thinNetwork`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` ## behaviour like connected.ppp U <- runiflpp(20, simplenet) plot(connected(U, 0.15, dismantle=FALSE)) ## behaviour like connected.owin ## remove some edges from a network to make it disconnected plot(simplenet, col="grey", main="", lty=2) A <- thinNetwork(simplenet, retainedges=-c(3,5)) plot(A, add=TRUE, lwd=2) X <- runiflpp(10, A) ## find the connected components cX <- connected(X) plot(cX[], add=TRUE, col="blue", lwd=2) ```